关于Hom-Leibniz代数胚表示  

On Representations of Hom-Leibniz Algebroids

作　　者：尹彦彬[1] 刘玲[2] 陈敏茹[1] 

机构地区：[1]河南大学数学与统计学院,河南开封475004 [2]北京信息科技大学理学院,北京100192

出　　处：《河南大学学报（自然科学版）》2015年第4期390-394,共5页Journal of Henan University:Natural Science

基　　金：北京市优秀人才培养资助项目(2012D005007000005)

摘　　要：Hom-Lie代数胚是李代数胚的一种自然推广,它的截面空间构成一个Hom-Lie代数,锚映射不再是截面空间同态.基于Hom-Lie代数胚概念定义了Hom-Leibniz代数胚,可以看作是非对称版本的Hom-Lie代数胚,即当截面空间的Hom-Jacobi代数反对称时,它就变为Hom-Lie代数胚.借鉴Leibniz代数的表示,定义了Hom-Leibniz代数胚的在向量丛上的表示.借助于直和空间投射,通过分析Hom-Leibniz代数胚Matched pair,构建了一对Hom-Leibniz代数胚的表示,并分析了它们的相容性条件.由于Hom-Lie代数胚是Hom-Leibniz代数胚的特殊情形,类似定义了Hom-Lie代数胚的表示及Matched pair,并获得了相应结果.Hom-Lie algebroid is a natural generalization of Lie algebroid. The space of its cross sections forms a Hom-Lie algebra, while the anchor is no longer a homomorphism between spaces of cross sections. Based on Hom- Lie algebroid, Hom Leibniz algebroid, which can be viewed as the non-symmetric version of Hom Lie algebroid, is defined. That is to say, it is in fact a Horn-Lie algebroid if the Hom-Jacobi algebra of space of cross sections is symmetric. Similar to the representation of Leibniz algebra, representation of Hom-Leibniz algebriod over vector bundle is also defined. By project maps of spaces of direct sum and from the analysis of matched pairs of Hom Leibniz algebroid, the representations of a pair of Hom Leibniz algebroids are constructed. Their corresponding conditions are also discussed. Since the Hom-Lie algebroid is a special case of Hom-Leibniz algebroid, the representation of Hom-Lie algebroid and the matched pair are defined similarly, and the corresponding results are also obtained.

关 键 词：Leibniz代数胚 Hom—Leibniz代数胚 Lie代数胚 Hom-Lie代数胚 

分 类 号：O186.1[理学—数学]